W. Which equation has both -2 and 2 as possible values of $$ x $$ ? $$ 4 imes \quad $$ A $$ x^{2}=4 $$ $$ 4 imes \quad $$ B $$ x^{3}=6 $$ $$ 4 imes \quad $$ C $$ x^{2}=2 $$ $$ 4 imes \quad $$ D $$ x^{3}=8 $$

Question

W. Which equation has both -2 and 2 as possible values of $$ x $$ ? $$ 4 	imes \quad $$ A $$ x^{2}=4 $$ $$ 4 	imes \quad $$ B $$ x^{3}=6 $$ $$ 4 	imes \quad $$ C $$ x^{2}=2 $$ $$ 4 	imes \quad $$ D $$ x^{3}=8 $$

UpStudy AI · Accepted Answer

To solve the problem, we want an equation that is satisfied by both $$ x = -2 $$ and $$ x = 2 $$.

**Step 1.** Check option A: $$ x^2 = 4 $$.

- Substitute $$ x = 2 $$ into the equation:
  $$
  2^2 = 4 \quad \Rightarrow \quad 4 = 4.
  $$
- Substitute $$ x = -2 $$ into the equation:
  $$
  (-2)^2 = 4 \quad \Rightarrow \quad 4 = 4.
  $$

Both values satisfy the equation.

**Step 2.** Verify that other equations do not satisfy both values.

- Option B: $$ x^3 = 6 $$
  - $$ 2^3 = 8 $$ (not equal to 6)
  - $$ (-2)^3 = -8 $$ (not equal to 6)

- Option C: $$ x^2 = 2 $$
  - $$ (2)^2 = 4 $$ (not equal to 2)
  - $$ (-2)^2 = 4 $$ (not equal to 2)

- Option D: $$ x^3 = 8 $$
  - $$ 2^3 = 8 $$ (satisfied)
  - $$ (-2)^3 = -8 $$ (not equal to 8)

Thus, only option A is valid.

**Answer:** A $$ x^2 = 4 $$
The equation $$ x^2 = 4 $$ is satisfied by both $$ x = -2 $$ and $$ x = 2 $$.

W. Which equation has both -2 and 2 as possible values of \( x \) ? \( 4 \times \quad \) A \( x^{2}=4 \) \( 4 \times \quad \) B \( x^{3}=6 \) \( 4 \times \quad \) C \( x^{2}=2 \) \( 4 \times \quad \) D \( x^{3}=8 \)

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